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When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
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Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
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Successive Refinement for Lossy Compression of Individual Sequences.

Neri Merhav1

  • 1The Viterbi Faculty of Electrical and Computer Engineering, Technion-Israel Institute of Technology, Technion City, Haifa 3200003, Israel.

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PubMed
Summary
This summary is machine-generated.

This study establishes outer bounds for successive-refinement coding using finite-state machines. Achievability schemes are proposed for both successive-refinement and multiple description coding problems.

Keywords:
Lempel-Ziv algorithmfinite-state machinemultiple description codingsuccessive refinement

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Area of Science:

  • Information Theory
  • Data Compression
  • Coding Theory

Background:

  • Lossy compression involves representing data with some information loss.
  • Successive-refinement coding allows for staged data compression and reconstruction.
  • Finite-state machines offer a model for practical compression algorithms.

Purpose of the Study:

  • To establish theoretical limits (outer bounds) for successive-refinement coding.
  • To develop practical coding schemes for successive-refinement and multiple description coding.
  • To analyze compression strategies using finite-state machine encoders.

Main Methods:

  • Deriving converse theorems to define achievable rate regions.
  • Developing constructive coding schemes for specific compression problems.
  • Extending existing methods for memoryless sources to more general cases.

Main Results:

  • Established outer bounds for successive-refinement coding with finite-state machines.
  • Proposed a straightforward achievability scheme for successive-refinement coding.
  • Developed analogous achievability schemes for the multiple description coding problem.

Conclusions:

  • The derived bounds provide fundamental limits for practical compression systems.
  • The proposed schemes demonstrate the feasibility of successive-refinement and multiple description coding.
  • This work advances the understanding of information-theoretic limits in data compression.